Marinade: Place all ingredients in a non-reactive bowl and whisk together.
Rub: Place all ingredients in a container with a lid and shake well.
Glue: Whisk ingredients together and place in a squeeze bottle.
Pork: Reserve 1 cup of marinade and set aside. (The reserved marinade will be used to base the pork during the cooking process.) Inject a little marinade into the pork butt in numerous places. Place pork in a resealable plastic bag and cover with remaining marinade. Marinate in the refrigerator for 6 to 8 hours.
Remove the pork from the marinade and pat dry with paper towels.
Cover pork with a light coat of the glue mixture to help the rub stick. Sprinkle generously with rub, making sure to work it into the meat.
Prepare a smoker to 225 to 250 degrees F and add the apple and hickory wood chips to the lit charcoal.
Place pork on smoker. Be careful not to over-smoke. After 2 hours, baste pork with reserved marinade and return it to the smoker for 1 hour. Baste again and return to smoker for 1 more hour. Repeat 1 more time, with the basting and smoking for 1 more hour. Remove pork from smoker, wrap in aluminum foil and return to smoker until the pork has an internal temperature of 200 degrees F. (Alternatively, you can finish cooking the pork in a low oven preheated to 250 degrees F). When the pork has reached 200 degrees F, remove it from the heat and let stand for approximately 15 to 20 minutes before slicing or pulling.